Physical consistency verification of power grid dispatching operations is crucial for ensuring system security. To address the challenge of detecting anomalies that are “data-correct but physically inconsistent” using traditional methods

this paper proposes a verification approach based on a multi-task learning physics-informed graph neural network (MTL-PI-GNN). Leveraging the inherent graph structure of power grids

this method models the grid topology as a graph and constructs a GNN surrogate model to learn the mapping from dispatching commands to power flow states. The power flow equation residual is incorporated as a physical regularization term to ensure the physical fidelity of the predictions. Furthermore

by establishing a unified physical consistency score

the approach enables quantitative assessment of whether dispatching operations conform to electrical laws. Simulation results demonstrate that MTL-PI-GNN significantly outperforms traditional methods in both power flow prediction accuracy and anomaly detection

validating the effectiveness and robustness of the proposed framework under various operating conditions.